Learn and practice the Graphs, Tries, and Custom Data Structures patterns to solve coding interview problems.

Educative-77 in C++: Accelerate Your Coding Interview Prep

Proficiency in advanced data structures is a marker of a highly experienced engineer, and interviewers use such questions to finetune how they grade candidates. This module teaches you the use of two advanced data structures—graphs and tries—to solve relatively complex problems. To solve problems with very specific requirements that may not be handled by standard data structures, we gain experience in the advanced skill of the design, implementation, and efficient use of custom data structures.

Advanced Data Structures

# Statement
You are given an array, `routes`, representing bus routes where `routes[i]` is a bus route that the $i^{th}$ bus repeats forever. Every route contains one or more stations. You have also been given the source station, `src`, and a destination station, `dest`. Return the minimum number of buses someone must take to travel from `src` to `dest`, or return `-1` if there is no route.

**Constraints:**

* $1 \le$ `routes.length` $\le 50$
* $1 \le$ `routes[i].length` $\le 100$
* $0 \le$ `routes[i][j]` $< 1000$
* $0 \le$ `src`, `dest` $< 1000$

# Examples

# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

What is the output if the following input is given?

Bus routes = [[4, 2, 12], [3, 26], [1, 10], [4, 26, 6]]

`src` = 3

`dest` = 12

What is the output if the following input is given?
Bus routes = [[4, 2, 12], [3, 26], [1, 10], [4, 26, 6]]
<code>src</code> = 3
<code>dest</code> = 12

What is the output if the following input is given?

Bus routes = [[5, 8, 1, 4], [7, 4], [9, 3, 2]]


`src` = 1

`dest` = 3

What is the output if the following input is given?
Bus routes = [[5, 8, 1, 4], [7, 4], [9, 3, 2]]
<code>src</code> = 1
<code>dest</code> = 3

What is the output if the following input is given?

Bus routes = [[4, 7, 9], [6, 8, 9]]

`src` = 4

`dest` = 8

What is the output if the following input is given?
Bus routes = [[4, 7, 9], [6, 8, 9]]
<code>src</code> = 4
<code>dest</code> = 8

# Figure it out!
We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

# Try it yourself
Implement your solution in the following coding playground.

#include <iostream>
#include <vector>
#include <queue>

int MinimumBuses(vector<vector<int>> busRoutes, int src, int dest)
{ 
 // Replace this placeholder return statement with your code
 return -1;
}

# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `MinimumBuses`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `C++`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `MinimumBuses` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `MinimumBuses`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `MinimumBuses`. \n- While calculating time complexity, include the time complexity of built-in C++ functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `MinimumBuses`. \n- While calculating space complexity, include the space complexity of built-in C++ functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

TwoDArray

#include <string>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

class TwoDArray : public DataStructure
{

 // define class attributes

private:
 void generateError(string data)
 {
 cerr << "MyConvert is not parsable: " << data;
 exit(-1);
 }

public:
 std::vector<vector<int>> val;

 TwoDArray()
 {
 // constructor
 }
 TwoDArray(std::vector<vector<int>> v)
 {
 this->val = v;
 // constructor
 }
 
 // return value will be passed to user program
 void *construct(string str, int typeOfDs)
 {
 json j_complete = json::parse(str);
 vector<vector<int>> temp = j_complete;
 this->val = temp;
 return this;
 // parse test case in json string 'value' to your desired data structure
 }

 // input param contains return value of user program
 string traverse(void *input, int typeOfDs)
 {
 return " ";
 // TwoDArray your data structure 'input' to a json string representing a test case output
 }

 // override operator<< for your data structure if required
};

def evaluate_results(self) -> object:
        """
        self.__inputs is the list of inputs that are passed as input to function
        self.__actual_output is a list of outputs that is produced by the learner's code
        return : self.__edu__result object
        """
        from collections import deque

        def minimum_buses2(routes, src, dest):
            adj_list = {}
            for i, stations in enumerate(routes):
                for station in stations:
                    if station not in adj_list:
                        adj_list[station] = []
                    adj_list[station].append(i)

            queue = deque()
            queue.append([src,0])
            visited_buses = set()
        
            while queue:
                station, buses_taken = queue.popleft()
                if station == dest:
                    return buses_taken
                
                if station in adj_list:
                    for bus in adj_list[station]:
                        if bus not in visited_buses:
                            for s in routes[bus]:
                                queue.append([s, buses_taken+1])
                            visited_buses.add(bus)                

            return -1

        def compareResult(expected, actual_output):
            
            if expected == actual_output:
                return True
            return False

        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = [] 
        # store the 1st expected output that should be displayed to the user 
        expected = minimum_buses2(self.__inputs[0], self.__inputs[1], self.__inputs[2])
        expected_outputs.append(expected)

        actual_output = self.__actual_outputs[0]
        compare = compareResult(expected, actual_output)
        if compare:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

#include "MinimumBuses.cpp"
#include "TwoDArray.cpp"


int MinimumBusesMain(TwoDArray v, int s, int d)
{
    int res = MinimumBuses(v.val, s, d);
    return res;
}

bus-routes.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [[2, 5, 7], [4, 6, 7]]
    - 2 : 2
    - 3 : 6
    output: 
    - 1 : 2
  - name: "testcase 2"
    inputs:
    - 1 : [[1, 12], [4, 5, 9], [9, 19],[10, 12, 13]]
    - 2 : 9
    - 3 : 12
    output:
    - 1 : -1
  - name: "testcase 3"
    inputs:
    - 1 : [[1, 12], [10, 5, 9], [4, 19], [10, 12, 13]]
    - 2 : 1
    - 3 : 9
    output:
    - 1 : 3
  - name: "testcase 4"
    inputs:
    - 1 : [[1, 9, 7, 8], [3, 6, 7], [4, 9], [8, 2, 3, 7], [2, 4, 5]]
    - 2 : 1
    - 3 : 5
    output:
    - 1 : 3
  - name: "testcase 5"
    inputs:
    - 1 : [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    - 2 : 4
    - 3 : 6
    output:
    - 1 : 1

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 def is_valid_2d_array(arr):
 if not isinstance(arr, list) or not all(isinstance(row, list) for row in arr):
 return False # Not a valid 2D array if it's empty or contains non-list elements
 
 for row in arr:
 if any(elem is None or isinstance(elem, bool) for elem in row):
 return False # Not a valid 2D array if any element in a row is None
 if not all(isinstance(elem, int) for elem in row):
 return False # Not a valid 2D array if any element in a row is not an integer
 
 return True # Valid 2D array
 
 lists = self.__inputs[0]
 if not is_valid_2d_array(lists):
 self.store_result ("Not a valid 2D array", ValidationFunction.FAIL)
 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 elif len(self.__inputs[0]) < 1 or len(self.__inputs[0]) > 50:
 self.store_result ("Length of bus routes array should be in range [1, 50]", ValidationFunction.FAIL)
 elif any(len(x) < 1 or len(x) > 100 for x in self.__inputs[0]):
 self.store_result("Bus stations array length should be in range [1, 100]", ValidationFunction.FAIL)
 elif any(x < 0 or x > 1000 for inner_array in self.__inputs[0] for x in inner_array):
 self.store_result("Bus stations array elements should be in range [0, 1000]", ValidationFunction.FAIL)
 elif self.__inputs[1] < 0 or self.__inputs[1] >= 1000:
 self.store_result("Source should be in range 0 <= src < 1000", ValidationFunction.FAIL)
 elif self.__inputs[2] < 0 or self.__inputs[2] >= 1000:
 self.store_result("Destination should be in range 0 <= dest < 1000", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Graphs

Trie

Custom Data Structures

Conclusion

Bus Routes

Statement

Examples

Understand the problem

Figure it out!

Try it yourself